Literally: that which stands beneath
I tried asking Fr. John today why hypostasis is so important in Orthodox theology. He got kind of excited, and said that way long ago it meant nature, but St. Basil the Great, in an extremely important act of theological genius (those weren’t his words, but he was very excited at this point; something about it being the most important meaning change in history) changed the meaning to person, because we do not and cannot know the nature of a being in the abstract, but only as manifested in particular persons. So Christ is a hypostatic union of humanity and divinity because he inseparably unites human and divine nature in a single person. But that’s still mysterious – perhaps necessarily so – hence, being an enigmatic rather than neglected word. One of these days I should find out what it was St. Basil wrote where he talked about that stuff.